Patent application title: WAVEFRONT SENSOR

Abstract:

The present invention relates to a wavefront sensor using a pair of
screens, each having a two-dimensional array of circular apertures, to
achieve Moire effects, and its use to measure the slope of a wavefront.

Claims:

1. An apparatus comprising:a) a first screen comprising a first
two-dimensional array of circular apertures, wherein the first screen is
placed downstream of a light source;b) a second screen comprising a
second two-dimensional array of circular apertures, wherein the second
screen is placed downstream of the first screen, the second screen is in
a plane parallel to the first screen, and the second screen is rotated
relative to the first screen; andc) a light detector downstream of the
second screen.

2. The apparatus of claim 1, wherein the first two-dimensional array and
the second two-dimensional array are identical.

3. The apparatus of claim 1, wherein at least one screen is a Hartmann
screen.

4. The apparatus of claim 3, wherein the first screen and the second
screen are Hartmann screens.

5. The apparatus of claim 1, wherein at least one screen is a
Shack-Hartmann lenslet array.

6. The apparatus of claim 5, wherein the first screen and the second
screen are Shack-Hartmann lenslet arrays.

7. The apparatus of claim 1, wherein the second screen is rotated about 1
to about 30 degrees relative to the first screen.

8. The apparatus of claim 1, further comprising a lens.

9. The apparatus of claim 8, wherein the lens is placed between the second
screen and the light detector.

10. The apparatus of claim 8, wherein the lens is placed upstream of the
first screen.

11. The apparatus of claim 1, further comprising a beam splitter
positioned upstream of the first screen.

12. A method of measuring characteristics of a lens comprising:a)
directing light into the lens;b) directing the light from the lens
through a first screen comprising a first two-dimensional array of
circular apertures;c) directing the light from the first screen through a
second screen comprising a second two-dimensional array of circular
apertures, wherein the second screen is placed downstream of the first
screen, the second screen is in a plane parallel to the first screen, and
the second screen is rotated relative to the first screen;d) detecting
the light from the second screen at a light detector.

13. The method of claim 12, wherein the first two-dimensional array and
the second two-dimensional array are identical.

14. The method of claim 12, wherein at least one screen is a Hartmann
screen.

15. The method of claim 14, wherein the first screen and the second screen
are Hartmann screens.

16. The method of claim 12, wherein at least one screen is a
Shack-Hartmann lenslet array.

17. The method of claim 16, wherein the first screen and the second screen
are Shack-Hartmann lenslet arrays.

18. The method of claim 12, wherein the second screen is rotated about 1
to about 30 degrees relative to the first screen.

19. The method of claim 12, further comprising directing the light through
a relay lens.

20. The method of claim 19, wherein the relay lens is placed between the
second screen and the light detector.

21. The method of claim 19, wherein the relay lens is placed upstream of
the first screen.

22. The method of claim 12, further comprising directing the light to a
beam splitter positioned upstream of the first screen.

23. A method of measuring characteristics of an eye comprising:a)
directing light into the eye;b) directing the light from the eye through
a first screen comprising a first two-dimensional array of circular
apertures;c) directing the light from the first screen through a second
screen comprising a second two-dimensional array of circular apertures,
wherein the second screen is placed downstream of the first screen, the
second screen is in a plane parallel to the first screen, and the second
screen is rotated relative to the first screen;d) detecting the light
from the second screen at a light detector.

24. The method of claim 23, wherein the first two-dimensional array and
the second two-dimensional array are identical.

25. The method of claim 23, wherein at least one screen is a Hartmann
screen.

26. The method of claim 25, wherein the first screen and the second screen
are Hartmann screens.

27. The method of claim 23, wherein at least one screen is a
Shack-Hartmann lenslet array.

28. The method of claim 27, wherein the first screen and the second screen
are Shack-Hartmann lenslet arrays.

29. The method of claim 23, wherein the second screen is rotated about 1
to about 30 degrees relative to the first screen.

30. The method of claim 23, further comprising directing the light through
a relay lens.

31. The method of claim 30, wherein the relay lens is placed between the
second screen and the light detector.

32. The method of claim 30, wherein the relay lens is placed upstream of
the first screen.

33. The method of claim 23, further comprising directing the light to a
beam splitter positioned upstream of the first screen.

[0002]A wavefront sensor is a device for measuring the aberrations of an
optical wavefront. Hartmann developed the Hartmann Test over one hundred
years ago, yet the Hartmann class of wavefront sensors continues to be
the most commonly used type of wavefront sensors to this time.

[0003]The first Hartmann Test was simply a screen, a sheet of material
with a series of holes cut into it. The Hartmann screen was placed at the
opening of a telescope and then viewed with the telescope's optics,
either lenses or mirrors. If there was any deviation in the location of
the holes of the Hartmann screen observed in the image of the Hartmann
screen created by the telescope optics, then a defect was present in the
telescope optics. In other words, aberrations were present in the
telescope optics.

[0004]Shack modified the Hartmann test by adding a lens (also called a
lenslet) into each of the holes in the Hartmann screen. The Hartmann
screen with lenslets is known as the Shack-Hartmann system. Each lenslet
has a controllable focal length, allowing a longer focal length than a
hole without a lens could create to be introduced into the system. A hole
with no lens will act as a pin-hole camera and cause a spot of light to
be formed some distance downstream in the direction of the flow of light.

[0005]Liang et al. modified the Shack-Hartmann system by adapting its use
to measuring the wavefront of the human eye. See U.S. Pat. No. 6,270,221.

[0006]The theory of operation when using a simple Hartmann screen as a
wavefront sensor is to pass light through the Hartmann screen, then
observe the location shift of the spots formed by the holes. The shift in
location of the spot is a direct indicator of the angle of the light that
passed through the hole, relative to the perpendicular axis. For example,
if light approached and then passed through the Hartmann screen
perpendicular to the flat surface of the screen (a flat wavefront), the
light would form a spot at a small distance downstream to the flow of
light, and the spot would appear to be in the center of the hole when
viewed from the downstream side of the Hartmann screen if the observer
was looking at the Hartmann screen perpendicularly. However, if the light
approached the Hartmann screen at an angle, for example, if the light
approached the screen such that the light's source was below the
perpendicular axis of the Hartmann screen and rising up, then the points
of light formed by the holes would be above the apparent center of the
holes of the Hartmann screen. With the use of basic trigonometry, the
distance of the lateral shift of the point of light, coupled with the
distance that the point of light is away from the hole, can be used to
calculate the angle of the approach of light. The spots of light form at
various distances downstream from the holes, and this must be either
measured or calculated in the conditions at which the light will be
analyzed. These distances are known to those skilled in the art of
optics.

[0007]In the case of measuring light in a manner useful to optical
applications, the complex shape of the light wave must be measured. In
these cases, each point of light is individually measured for movement,
and the angle of light, or in other words, its slope, can be measured at
each of the numerous individual locations, allowing a complex analysis to
occur.

[0008]The angle (or slope) of the approaching light to be analyzed is
usually very small in most optical applications. For example, with human
eyes, refraction is measured in diopters. If, for example, an eye had one
diopter of refractive error, the angle of the light to be measured from a
six mm pupil is only one third of a degree. If light from this eye were
passed through a Hartmann screen and formed a spot of light at a distance
of 4 mm downstream, the spot will have shifted off-center by only 0.023
mm. Such a small shift can be difficult to detect and measure.

[0009]When lenses are added to the Hartmann screen (a Shack-Hartmann
wavefront sensor), the distance between the spot of light and the screen
can be increased, thereby increasing the lateral movement of the spots
for any given angle of light approaching the device. This axial distance
could be controlled by the focal distance of the lens. For example, if
the same one diopter light beam described in the preceding paragraph were
used with typical Shack-Hartmann lenslet array with lenses having a 20 mm
focal distance, the spot would shift 0.115 mm laterally (vs. 0.023 mm
along a 4 mm axial distance). This increased lateral movement of 500%
results in a 500% improvement to the sensitivity of the system.

[0010]However, this increase in sensitivity comes at the price of reducing
the range of measurement of the device. By extending the distance that
the spots of light formed away from the Hartmann screen, the
Shack-Hartmann wavefront sensor causes a simultaneous increase in the
variability of the shift in the axial distance that occurs along with the
shift in the lateral distance, causing the spots to become no longer in
the focus plane of the observing camera, which is used to detect the spot
movement. With both systems, the Hartmann Screen and the Shack-Hartmann,
as the spots of light shift laterally, they also shift axially, or
lengthwise. For example, with a diverging wavefront passing through the
system, the spots of light will all appear to be moving radially outward
from each other, but they will also be moving further downstream from the
holes and/or the lenses. In the case of the Hartmann Screen, the movement
in both directions, laterally and axially, is less than the amount of
movement caused by the Shack-Hartmann device. The axial movement of the
Hartmann Screen spots is considerably less than the axial movement of the
Shack-Hartmann spots, and consequently, the spots remain in focus of the
observing camera throughout a higher range of measurement than the
Shack-Hartmann device.

[0011]Hence, the Hartmann Screen has higher dynamic range of measurement
but lower sensitivity to small light shifts, while the Shack-Hartmann
system has lower dynamic range of measurement but higher sensitivity to
small light shifts. Increased sensitivity comes at the expense of range,
and increased range comes at the expense of sensitivity in these devices.

[0012]Many efforts have been made to overcome this deficiency in the
Shack-Hartmann system. A review of the literature in the public domain
will yield many examples of such efforts, but all of these efforts
require that the system be made more complex with such things as moving
optical parts, higher resolution, more expensive cameras, complex
sub-pixel analysis, etc.

[0013]A different optical system is the Talbot wavefront sensing method
(also a concept known for more than one hundred years). Talbot optics are
optics made from rulings (a series of parallel lines cut into or etched
onto a clear object), or cross gratings, which are two sets of parallel
rulings intersecting each other at a cross angle, which cause a
self-imaging pattern of lines or cross lines to form in space a predicted
distance away from the Talbot optic called "shadow patterns," with the
distance based upon factors such as the wavelength of light and the
spacing of the ruling lines. The location of these shadow lines would
move based upon the angle of light passing through the Talbot optic, but
they too would move only small amounts.

[0014]To increase the movement of the shadow patterns, the Moire effect
was employed with the Talbot (or other shadow-creating) optics. U.S. Pat.
No. 5,963,300 to Horwitz and U.S. Pat. No. 6,736,510 to Van Heugten
describe Talbot wavefront sensing systems with the use of Moire effects.
Horwitz placed a second, identical Talbot optic behind the first Talbot
optic, then rotated the second Talbot optic slightly with respect to the
first Talbot optic. By doing so, the shadow pattern's movement was
amplified, making the movement easier to detect. Both devices described
in these patents used rulings or gratings to produce shadows and did not
use Hartmann optics with circular apertures to produce light spots of
concentrated, focused beams.

[0015]A moving shadow pattern (as in Talbot or Talbot Moire) differs from
the moving spots (as in the Hartmann Screen or the Shack-Hartmann
device). Hartmann screens do not merely form shadows or shadow patterns,
they form focused spots of light due to the holes acting as pinhole
cameras, concentrating a beam diameter down to a smaller beam diameter,
or a point. Shack-Hartmann devices also do not form shadow patterns; they
form focused spots of light due to the lenslets refracting the light,
also concentrating a beam diameter down to a smaller beam, or a point.
The moving shadow patterns are not as localized and can not be measured
for centration as well as the moving spots of Hartmann devices. Other
advantages of moving spots versus shadows include that Hartmann-based
optics can form spot patterns of light at a narrower plane from
polychromatic light, whereas Talbot optics create a thicker plane which
cannot be imaged by a camera as easily, if at all. This allows
Hartmann-based optics to examine beams of light in multiple wavelengths
if necessary, which is particularly useful when measuring the human eye,
whereas Talbot based optics are limited to function in narrower
wavelength bands of light. Another advantage is that in today's wavefront
sensor, CCD cameras are used to view the images. CCD cameras have square
pixels aligned in rows and columns, causing aliasing distortions when the
shadow lines formed by Talbot optics that utilize rulings or gratings
align with the rows of pixels, which interferes with the analysis.
Hartmann-based optics create circular spots, which do not create this
aliasing problem. Another advantage of Hartmann-based optics is that
because the spots formed are circular, more efficient centroiding
algorithms may be used, which cannot be used as efficiently upon the
lines or squares formed by Talbot optics.

[0016]There is a need for wavefront sensors that can achieve both high
sensitivity and a high dynamic range of measurement. There is also a need
for wavefront sensors that result in a high image quality. There is also
a need for wavefront sensors that are small, lightweight, inexpensive,
versatile, and simple.

BRIEF SUMMARY OF THE INVENTION

[0017]The present invention is directed to an apparatus comprising two
screens, each having a two-dimensional array of circular apertures,
wherein the second screen is rotated with respect to the first screen,
thereby creating a Moire effect.

BRIEF DESCRIPTION OF THE DRAWINGS

[0018]FIG. 1 shows an exemplary optical layout of the components from a
side perspective.

[0019]FIG. 2 shows an alternative optical layout, also from a side
perspective.

[0022]FIG. 5 shows an optical layout for determining the best distance
between the two screens.

[0023]FIG. 6 shows an exemplary spot pattern created by a plane light wave
passing through the layout depicted by FIG. 1.

[0024]FIG. 7 shows a Point Grey FL2 CCD camera photograph of the exemplary
spot pattern created by a plane light wave passing through the layout
depicted by FIG. 1.

[0025]FIG. 8 shows an exemplary spot pattern created by a cylindrical
light wave passing through the layout depicted by FIG. 1.

[0026]FIG. 9 shows a Point Grey FL2 CCD camera photograph of the exemplary
spot pattern created by a cylindrical light wave (i.e., the beam has an
astigmatism) passing through the layout depicted by FIG. 1.

[0027]FIG. 10 shows an exemplary spot pattern created by a purely
spherical light wave passing through the layout depicted by FIG. 1.

[0028]FIG. 11 shows a Point Grey FL2 CCD camera photograph of the
exemplary spot pattern created by a converging light wave passing through
the layout depicted by FIG. 1.

[0029]FIG. 12 shows a Point Grey FL2 CCD camera photograph of the
exemplary spot pattern created by a diverging light wave passing through
the layout depicted by FIG. 1.

[0030]FIG. 13 shows a Point Grey FL2 CCD camera photograph of the
exemplary spot pattern created by a spherical aberrated light wave
passing through the layout depicted by FIG. 1.

[0031]FIG. 14 shows a Point Grey FL2 CCD camera photograph of the image
formed when two Hartmann screens are positioned at zero degrees rotation.

[0032]FIG. 15 shows a Point Grey FL2 CCD camera photograph of the image
formed when two Hartmann screens are positioned at one degree rotation.

[0033]FIG. 16 shows a Point Grey FL2 CCD camera photograph of the image
formed when two Hartmann screens are positioned at two degrees rotation.

[0034]FIG. 17 shows a Point Grey FL2 CCD camera photograph of the image
formed when two Hartmann screens are positioned at four degrees rotation.

[0035]FIG. 18 shows a Point Grey FL2 CCD camera photograph of the image
formed when two Hartmann screens are positioned at six degrees rotation.

[0036]FIG. 19 shows a Point Grey FL2 CCD camera photograph of the image
formed when two Hartmann screens are positioned at eight degrees
rotation.

[0037]FIG. 20 shows a Point Grey FL2 CCD camera photograph of the image
formed when two Hartmann screens are positioned at ten degrees rotation.

[0038]FIG. 21 shows a Point Grey FL2 CCD camera photograph of the image
formed when two Hartmann screens are positioned at twelve degrees
rotation.

[0040]FIG. 23 shows measurements to assure tight alignment tolerance for
the testing of trial lenses. The amount of measured cylinder was measured
using a sphere lens from about -20 D to +18 D with fixed scheme.

[0041]FIG. 24 shows the results of a comparison of measurement and tested
trial lenses for spherical test lenses from -20 D to +18 D (correlation
coefficient r=1.000). From -0.75 D to +0.75 D, the increments of the test
lenses was 0.125 D.

[0048]FIG. 31 shows the results of a repeatability test for cylindrical
test lenses from -8 D to +8 D. Maximum deviation was less than 0.03 D.

[0049]FIG. 32 shows a CCD camera photograph of the shadow patterns created
by a comparative Talbot-Moire wavefront sensor, wherein the two Talbot
optics are configured to produce similar sized spot patterns as those
depicted in the following Figure.

[0050]FIG. 33 shows a CCD camera photograph of the spot patterns created
by a Hartmann-Moire wavefront sensor configured to produce similar sized
spot patterns as those depicted in the preceding Figure.

[0051]FIG. 34 shows a CCD camera photograph of the shadow patterns created
by a comparative Talbot-Moire wavefront sensor, wherein the two Talbot
optics are configured to produce similar sized spot patterns as those
depicted in the following Figure.

[0052]FIG. 35 shows a CCD camera photograph of the spot patterns created
by a Hartmann-Moire wavefront sensor configured to produce similar sized
spot patterns as those depicted in the preceding Figure.

[0056]The novel wavefront sensor described herein utilizes two screens
that are rotated relative to each other to create Moire effects to
amplify the movement of the spots created by a light beam passing through
a Hartmann screen. By rotating the two screens, the axial (lengthwise)
distance that the spots form downstream from the screen may be reduced by
design, allowing greater dynamic range of measurement. Simultaneously,
the lateral movement is increased, allowing greater sensitivity to
measure smaller wavefront slopes.

[0057]In one embodiment, the apparatus of the present invention comprises:
a first screen comprising a first two-dimensional array of circular
apertures, wherein the first screen is placed downstream of a light
source; a second screen comprising a second two-dimensional array of
circular apertures, wherein the second screen is placed downstream of the
first screen, the second screen is in a plane parallel to the first
screen, and the second screen is rotated relative to the first screen;
and a light detector downstream of the second screen.

[0058]As shown in FIG. 1, the first screen (10) is placed downstream of a
light beam to be analyzed, a second screen (15) is placed downstream of
the first screen, and a light detector (20) is placed downstream of the
second screen. "Downstream" means further from the light beam's source on
the path traveled by the light beam. In one embodiment, the light source
will project a plane light wave (5) that propagates from left to right,
becomes incident upon a first Hartmann screen (10), passes through the
first Hartmann screen (10), becomes incident upon a second Hartmann
screen (15), passes through the second Hartman screen (15), and then
becomes incident upon the light detector (20). In one embodiment, the
holes of the second screen (15) are on the right side of the optic in the
drawing orientation of FIG. 1.

[0059]In one embodiment, the light detector (20) can convert light to
electronic signals, which can be fed into a computer for analysis.
Methods of feeding such data into a computer are known to those skilled
in the art of Machine Vision. For example, a charge-coupled device (CCD)
light detector, such as a Watec LCL 903 K CCD camera, Point Grey FL2 CCD
camera, or other commercially available CCD camera, can be connected to
an IMperx Frame Grabber, or other commercially available frame grabber,
that allows the light images to be placed into computer memory for
analysis.

[0060]FIG. 2 shows an alternative embodiment for allowing light detector
(20) to accept and convert the light to electronic signals. A relay lens
(17) is placed between the second screen (15) and the light detector
(20), allowing the spot patterns formed by the second screen (15) to come
into focus upon the light detector (20). Another position for a relay
lens can be upstream of the first screen, e.g., between the light source
(5) and the first screen (10). One or more lenses can be placed in one or
both of these positions. Such relay optics and their design are known to
those skilled in the art of optics design. An exemplary lens (17) is an
Edmund Optics Triplet with a focal distance of 25 mm.

[0061]Each screen comprises a two-dimensional array of circular apertures.
The two-dimensional array of circular apertures can include, for example,
an array of rows and columns, but the circular apertures may be arranged
in other orthogonal or non-orthogonal two-dimensional arrays. The first
and second screens can have an array that is the same as, or in some
cases, different from one another.

[0062]Either one or both of the screens can be Hartmann screens. In one
embodiment, both of the screens are Hartmann screens. FIG. 3 shows an
example layout of a Hartmann screen. Clear glass substrate (25) is coated
with an opaque coating (30) with multiple holes such as hole (35) made
clear into the opaque coating (30). Preferably, holes such as hole (35)
are arranged in a repeating array pattern with horizontal and vertical
spacing, as well as hole diameter, in a consistent pattern. For example,
a preferred embodiment would have holes of 0.001 inch diameter clear
zone, spaced 0.002 inches apart, center to center, aligned in an
orthogonal pattern. An example of substrate (25) is 0.062 inch thick
Schott Glass, and an example of opaque coating (30) is chrome applied by
vapor deposition.

[0063]Different holes sizes and hole spacing can be used. Preferably, each
hole has a diameter of about 0.0001 inch to about 0.01 inch, about 0.0002
inch to about 0.005 inch, or about 0.001 inch. Preferably, the holes are
spaced apart by about 0.0002 inch to about 0.02 inch, about 0.0004 inch
to about 0.01 inch, or about 0.002 inch. The hole size and hole pattern,
in addition to the degree of rotation, are selected to create a Moire
effect.

[0064]Coating thicknesses can also vary. Preferable coating thicknesses
include about 0.00001 inch to about 0.01 inch, about 0.0025 inch to about
0.0075 inch, or about 0.005 inch.

[0065]One or more of the circular apertures can include a lens (lenslet).
Preferably, each lenslet has the same positive focal length. In one
embodiment, each circular apertures of one array comprises a lens. Such
an array is called a Shack-Hartmann Lenslet Array. In another embodiment,
both screens are Shack-Hartmann Lenslet Arrays.

[0066]The device can further include a beam splitter. Preferably the beam
splitter is positioned upstream of the first screen, e.g., between the
first screen and a light source. The beam splitter can facilitate
directing the light beam, which may be particularly useful when measuring
the characteristics of an eye.

[0067]FIG. 4 shows a perspective view of how the first screen (10) is
oriented with respect to the second screen (15), which is a slight
rotation to each other. The center of each optic would remain in the same
location along the Z axis (18), and the plane of each optic would remain
parallel to each other, but the orientation of rotation would occur in
the remaining degree of freedom. These terms are known to those skilled
in the art of optics design. Furthermore, one of ordinary skill in the
art would understand that the screen rotation can also be achieved by
rotating the array portion rather than rotating the entire substrate of
the screen.

[0068]The degree of rotation is sufficient to create a Moire effect and to
create a detectable image of the spots. Preferably, the degree of
rotation is about 1 to about 30 degrees, about 3 to about 20 degrees,
about 6 to about 18 degrees, about 10 to about 14 degrees, or about 12
degrees.

[0069]The rotated screens can be achieved, for example, by the following
process: lay the first screen (10) flat on a surface, then lay the second
screen (15) flat upon the first screen (10) such that maximum contact
surface area is achieved. With both screens still touching, rotate the
second screen (15) while maintaining the same amount of contact surface.
Then, introduce a distance between the screens during the assembly
process, as depicted by FIG. 1.

[0070]As shown in FIG. 5, to determine a gap between the first screen (10)
and the second screen (15), temporarily remove the second screen (20) and
replace it with light detector (20), placing light detector (20) as close
as possible to first screen (10). Allow a plane wave of light
perpendicular to the Z axis to pass through the first screen (10), then
move light detector (20) further and closer away from the first screen
(10) while observing the spots being detected by light detector (20).
Select a distance between the light detector (20) and the first screen
(10) at which distinct spots are being detected by light detector (20).
To fine tune the setup, replace plane wave (5) with light of the type and
vergence that will be analyzed in the application, and repeat the above
distance setting tests. Depending upon conditions, several different
distances may be discovered to work well. As a general rule, longer
distances provide higher sensitivity, and closer distances provide higher
dynamic range of measurement. Also, one distance may provide more dynamic
range in one direction of vergence or divergence measurement, while
another may provide more dynamic range in the opposite direction of
vergence or divergence. After a suitable distance is selected, remove the
light detector (20), and replace it with the second screen (15) at the
distance and location selected, as described above. Replace light
detector (20) at its appropriate position described in FIG. 1 or FIG. 2.

[0071]Once assembled in this configuration, further distances and rotation
angles may be tested by moving first screen (10) and second screen (15)
so that the two surfaces with the etched holes are in contact with each
other, and some angle between the two is selected, such as 3 degrees.
Then place within the beam of light, before it is incident upon first
screen (10), a lens with a 200 mm positive focal length (i.e., 5
Diopters), and observe that there is no movement of the spots. Then,
slowly move the first screen (10) away from second screen (15) while
placing into the beam and then removing from the beam the 200 mm positive
focal length lens and observing the movement of the spots at each
distance between the two screens. As first screen (10) moves further away
from second screen (15), the amount of movement of the spots will
increase (i.e., the system will become more sensitive to the light
angle). Once a desired distance is selected, the rotation of the two
screens may be adjusted. As the angle between the two screens increases,
the density of the spot pattern in increases, but the amount of movement
of the spots per diopter of light angle will decrease. FIGS. 14-21 show
the variation in spot pattern density under various rotations. During
these various setup conditions, one can expose the setup to a range of
light conditions expected to be seen during use and select the setup
conditions that produces the combination of the most distinct spot
patterns coupled with the amount of movement of spots per diopter of
light vergence or divergence that will best yield the required
sensitivity.

[0072]Of the many possible configurations, one exemplary setup that works
when analyzing light beams in the central portion of the visible spectrum
(e.g., green at 532 nm) is to have first and second screens, flat
surfaces parallel to each other but rotated 12 degrees to each other,
each having 0.001428 inch diameter holes spaced 0.002857 inches apart,
center to center, with an optical distance of 0.024 of an inch between
the first and second screens, and the light detector (e.g., a camera) set
up to image the plane of where the holes are on the second screen.

[0073]The image quality achieved by the Hartmann-Moire system can
advantageously surpass the image quality achieved by a Talbot-Moire
system. The amount of spot movement in the Hartmann-Moire system is
directly proportional to the refractive power being observed by the
system. However, the Talbot-Moire system requires that the second Talbot
optic be placed at a specific, calculated distance away from the first
Talbot optic, described by the following formula: Distance=period squared
divided by the wavelength of the light. The period is the distance
between the holes. In the example described in the preceding paragraph,
the second Talbot optic must be placed 0.097 inch away from the first
Talbot optic, and it will not function properly if it is any closer. In
contrast, Hartmann screens can be placed much closer to one another and
at many more locations where it will operate properly.

[0074]The distance between screens in a Hartmann-based system is not
constrained by this Talbot formula, proving that it works under a
different set of principles of physics. The Hartmann-Moire system
described herein will work at the same distance that the Talbot-Moire
formula prescribes, but it also works at many other distances that would
not work with Talbot-Moire system. This flexibility of distances allows
measurements of a wider spectrum of light wavelength. Also, a smaller
distance between screens can be used with the Hartmann-Moire system. This
can be quite useful in optical applications wherein the observer or
camera must simultaneously view the image of an eye and the spot pattern.
The image of the eye comes into focus at the first screen, but the spots
are in focus at the second screen, which is where the camera focuses. If
the distance between the two screens is too great, the eye becomes out of
focus to the camera. When this distance can be made shorter, as in the
present system, then the image of the eye formed at the first screen can
be in better focus to the camera that is focused at the second screen,
providing a compound image of both the eye and the spots, with the spots
superimposed over the eye image. This allows for a more precise
determination of the refractive power of the eye at each particular spot
location because each spot can be associated with a particular
corresponding location of the eye.

[0075]In one embodiment, the invention provides a large dynamic range of
measurement and/or a high level of sensitivity to measure smaller
wavefront slopes. Preferably, the invention provides both a large dynamic
range of measurement and a high level of sensitivity to measure smaller
wavefront slopes. In particular, the invention can be configured to
provide a measurement accurate within about 0.5 D, 0.4 D, 0.3 D, 0.25 D,
0.23 D, 0.2 D, or 0.1 D over a range of about 5 D, 7 D, 10 D, 11 D, 15 D,
16 D, 17 D, 18 D, 20 D, 24 D, 30 D, 35 D, 38D, or 40 D, or other
increments within these ranges.

[0077]FIG. 6 shows a field of view (40) (the image that light detector
(20) produces) having an exemplary array of spots produced by a planar
wave of light that passed through both screens. The distance between all
of the spots increases as the relative rotation angle between the first
screen and the second screen decreases in angle, and the distance
decreases as the rotation increases. Example spot (45) is shown in an
example location. The location of each spot is recorded with a known beam
of light being examined by the entire device. Each spot of light will
move in direction and magnitude in relation to the change of the slope of
the light that has passed through the device in the zone being
represented by that spot. In other words, if all the spots move
uniformly, the entire beam of light possesses the same change in slope
across it, in a uniform pattern. If some spots move more or less than
others, that indicates a more or less change of slope for the area that
that particular spot represents.

[0078]One of ordinary skill in the art, e.g., one familiar with Machine
Vision and computer programming, knows how to instruct a computer to
measure the movement of the spots. Commercially available programs such
as Matlab, or other available source code for spot centering, provide
such routines.

[0079]If the planar light beam used in FIGS. 6 and 7 is replaced with a
light beam having an astigmatism, the spot would move to a new location
as shown by example spot (50) in FIGS. 8 and 9. The pattern of spots in
the field of view (40) shown in FIG. 8 is an example of pure cylinder
deviation, which is a term understood by those skilled in the art of
optics design.

[0080]If the planar light beam used in FIGS. 6 and 7 is replaced with a
light beam having a purely spherical change to its slope, the exemplary
spot pattern would appear as in FIGS. 10-12.

[0081]If the planar light beam used in FIGS. 6 and 7 is replaced with a
light beam having spherical aberration in its slope, the exemplary spot
pattern would appear as in FIG. 13.

[0082]To calibrate the system, the preferred method is to pass a plane
wave of light through the system and record the location of all the
spots. Then pass a series of different light beams through the system
with known amounts of sphere and cylinder changes, and record the
movement of each of the spots at each location under each light beam
condition. From this calibration, the relationship of the movement of the
spots to the slope change of the light beam being analyzed can be
quantified, then used for the computation step when the device is used in
service. One of ordinary skill in the art of optics design knows how to
create various optical wavefronts for this calibration method. One way to
do so would be to purchase a 25 mm diameter collimated laser beam from
such suppliers as Newport Optics, Melles Griot, or Thor Labs, and then
purchase an Optometrists Trial Lens set from any ophthalmic or optometric
supplier such as Reichert, American Optical, or other vendors, then place
these trial lenses within the laser beam.

[0083]The device described above can be used to measure the slope of a
wavefront. The device can be used in a variety of optical applications,
such as measuring the characteristics of a lens, including an eye. A
method of measuring characteristics of a lens comprises: directing light
into the lens; directing the light from the lens through a first screen
comprising a first two-dimensional array of circular apertures; directing
the light from the first screen through a second screen comprising a
second two-dimensional array of circular apertures, wherein the second
screen is placed downstream of the first screen, the second screen is in
a plane parallel to the first screen, and the second screen is rotated
relative to the first screen; and detecting the light from the second
screen at a light detector. Similarly, the device can be used to measure
the characteristics of an eye by first directing light, e.g., a small
diameter beam of light, into an eye. The eye reflects the beam out, and
then the reflected beam is directed into the first and second
two-dimensional arrays and a light detector. These methods can be used
with any of the device embodiments described herein.

[0084]The present invention is further described by the following
non-limiting examples.

EXAMPLE 1

Testing the Wavefront Sensor with Spherical and Cylindrical Trial Lenses

[0085]Data were measured at a wavelength of 532 nm without focus
adjustment so that the full range of wavefront vergences was presented to
the wavefront sensor. The accuracy and dynamic range of the
Hartmann-Moire wavefront sensor was evaluated by measuring defocus and
astigmatism induced by a series of standard Topcon spherical lenses
(e.g., 77 lenses from -20 D to +18 D) and cylindrical trial lenses (e.g.,
16 lenses from -8 D to 8 D). Repeatability of the Hartmann-Moire
instrument was assessed by taking 3 repeated measurements within a
2-minute period. Measured trial lens values with the Hartmann-Moire
wavefront sensor were compared to lens values verified with a standard
lensometer. Analyses were based on a 4-mm pupil diameter specified in the
software. The test configuration is shown in FIG. 22.

[0086]Measurements should be taken to assure tight alignment tolerance
(decentration tilt). For example, for accuracy of 0.5 D measured at -20
D, the axial tolerance should be 1.28 mm. As shown in FIG. 23, the amount
of measured cylinder was measured using a sphere lens from about -20 D to
+18 D with fixed scheme (mean=0.04 D, maximum=0.17 D).

[0087]Defocus was accurately measured over a 38 D range and astigmatism
over a 16 D range. Correlation coefficients between mean wavefront
measurements (n=3) and expected refractions for both sphere and cylinder
lenses were 1.00.

[0088]For spherical lenses, the instrument was accurate to within 0.2 D
over the range from -20 D to +18 D without any means to compensate
refraction. Results for spherical test lenses are shown in FIGS. 24-27.

[0089]For cylindrical lenses, the instrument was accurate to within 0.15 D
over the range from -7 D to +10 D without any means to compensate
refraction. The amplitude of measured astigmatism was accurate to within
0.33 D within the range of 16 D (-8 D to +8 D) without any means to
compensate refraction. The amplitude of measured astigmatism was accurate
to within 0.2 D within the range of 11 D (-3 D to +5 D) without any means
to compensate refraction. Results for cylindrical test lenses are shown
in FIGS. 28-31.

[0090]The repeatability for fixed condition measurements obtained within 2
minutes was within 0.03 D. Improved accuracy would be expected after an
optimized calibration that takes component tolerances into account.

[0091]These results demonstrate that the Hartmann-Moire wavefront sensor
measures defocus and astigmatism accurately and repeatedly over a large
dynamic range of -20 D to +18 D for spherical lenses and over the range
of -8 D to 8 D for cylindrical lenses.

EXAMPLE 2

Comparison of Hartmann-Moire to Talbot-Moire

[0092]FIGS. 32-35 demonstrate the improved image quality achieved by the
Hartmann-Moire wavefront sensor described herein as compared with a
Talbot-Moire wavefront sensor. FIGS. 32 and 34 show CCD camera
photographs of the shadow patterns created by a Talbot-Moire wavefront
sensor. FIGS. 33 and 35 show CCD camera photographs of the spot patterns
created by a Hartmann-Moire wavefront sensor configured to produce
similar sized spots as the shadows depicted in FIGS. 32 and 34,
respectively.

[0093]As shown by the comparative figures, the spots formed by the
Hartmann-Moire wavefront sensor are of a high image quality, allowing for
a more accurate determination of each spot's center and a more accurate
measurement of the spot's movement and position.

EXAMPLE 3

Comparative Examples for Measuring a Model Eye

[0094]FIG. 36 shows two images from a comparative Shack-Hartmann device.
FIG. 36A shows spots of light formed when a plane wave is being measured
(i.e., an emmetropic eye), and FIG. 36B shows spots of light formed when
the model eye has a converging beam of light emerging from it (i.e., a
myopic eye). As the beam of converging light passes through the
Shack-Hartmann device, the spots grow closer together, and the amount
that they have moved is easily observed. However, at the relatively low
optical power of only four Diopters, the spots of light begin to lose
their contrast and become blurry. This makes the task of determining the
centroid of the spot of light difficult, if not impossible. As the power
of the converging light grows beyond four Diopters, the spots of light
will get even more blurry, to the point of where the device can no longer
make a measurement, which is why this device has a low dynamic range.

[0095]FIG. 37 shows two images from a comparative Hartmann Screen device.
FIG. 37A shows spots of light formed when a plane wave is being measured
(i.e., an emmetropic eye), and FIG. 37B shows spots of light formed when
the model eye has a converging beam of light emerging from it (i.e., a
myopic eye). As the beam of converging light passes through the Hartmann
device, the spots grow closer together, but the amount that they have
moved is very small. Although at the relatively high optical power of ten
Diopters the spots continue to have high contrast and are in sharp focus,
the amount of movement of the spots is much smaller than the amount of
movement of the spots in the Shack-Hartmann device, which is why this
device has low sensitivity.

[0096]FIG. 38 shows two images from a Hartmann-Moire device as described
herein. FIG. 38A shows spots of light formed when a plane wave is being
measured (i.e., an emmetropic eye), and FIG. 38B shows spots of light
formed when the model eye has a converging beam of light emerging from it
(i.e., a myopic eye). As the beam of converging light passes through the
Hartmann-Moire device, the spots rotate clockwise, and the amount that
they have moved is easily observed. Even at the relatively high optical
power of ten Diopters the spots continue to have high contrast and are in
sharp focus, which is why this device has both high sensitivity and a
high dynamic range.